The concept of fractal, such as Cantor set, has been combined with the Fresnel zone plates (ZPs) to improve its imaging
capability and introduce additional freedom for optimizing. In this letter, Fibonacci zone plates (FiZPs), which is
generated by means of Fibonacci fractals, was proposed. The FiZPs can be constructed by the generating rules of the
Fibonacci sequences similar with the Cantor set zone plate published. Numerical simulation based on Fresnel diffraction
is performed to verify the on-axis intensity distribution of the FiZPs. According to the simulated results, the FiZPs can
focus the incident beam as conventional zone plates as well but with fractal on-axis intensity profile. The theoretical
results are also verified by the experiment by means of phase-only spatial light modulator (pSLM).
Furthermore, the spiral Fibonacci zone plate (sFiZPs) was designed by overlapping the spiral phase on the FiZPs. Both
numerical simulations and experiments are performed and the results are coincident well with each other.